Advisers who represent what remains of Gawker Media Group in bankruptcy are exploring whether they can bring a viable lawsuit against Peter Thiel, the Silicon Valley billionaire who helped finance Hulk Hogan’s successful legal battle against the publisher.

Gawker on Tuesday asked a bankruptcy judge for permission to subpoena Mr. Thiel to obtain information upon which it may build a possible legal case against him. Gawker is also seeking information from Charles Harder, the lawyer who represented Hulk Hogan, as well as others...